I measured the pH of distilled water, expecting it to be 7.0, but instead it came out way different! Is something wrong with my equipment?

Don’t frustrate yourself trying to interpret the pH of pure water.  In principle, very pure water should indeed have a pH of 7.0, but usually it is 5 to 6 because atmospheric CO2 dissolves readily into the water to produce carbonic acid.  Some deionizers will produce perfectly pure water that is nevertheless slightly alkaline, pH 7.5 – 8.  Check your pH calibration instead with cream of tartar.